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About: Random Vectors and Joint Distributions

Module by: Paul E Pfeiffer. E-mail the author

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Name: Random Vectors and Joint Distributions
ID: m23318
Language: English (en)
Summary: Often we have more than one random variable. Each can be considered separately, but usually they have some probabilistic ties which must be taken into account when they are considered jointly. We treat the joint case by considering the individual random variables as coordinates of a random vector. We extend the techniques for a single random variable to the multidimensional case. To simplify exposition and to keep calculations manageable, we consider a pair of random variables as coordinates of a two-dimensional random vector. The concepts and results extend directly to any finite number of random variables considered jointly. If the joint distribution for a random vector is known, then the distribution for each of the component random variables may be determined. These are known as marginal distributions. In general, the converse is not true. However, if the component random variables form an independent pair, the treatment in that case shows that the marginals determine the joint distribution.
Subject: Mathematics and Statistics
Keywords: applied probability, joint distribution, random variables, random vectors
License: Creative Commons Attribution License CC-BY 3.0

Authors: Paul E Pfeiffer (perhp@earthlink.net)
Copyright Holders: Paul E Pfeiffer (perhp@earthlink.net)
Maintainers: Paul E Pfeiffer (perhp@earthlink.net), Daniel Williamson (dcwill@cnx.org), C. Sidney Burrus (csb@rice.edu)

Latest version: 1.8 (history)
First publication date: Apr 16, 2009 12:27 pm -0500
Last revision to module: Sep 18, 2009 1:50 pm -0500

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Version History

Version: 1.8 Sep 18, 2009 1:50 pm -0500 by Daniel Williamson
Changes:
added google analytics tracking code

Version: 1.7 Jul 27, 2009 5:37 pm -0500 by Paul E Pfeiffer
Changes:
Summary updated

Version: 1.6 Jul 27, 2009 5:24 pm -0500 by Paul E Pfeiffer
Changes:
Summary added

Version: 1.5 Jul 27, 2009 12:12 pm -0500 by Daniel Williamson
Changes:
disjoint union fix

Version: 1.4 Jun 19, 2009 11:33 am -0500 by Daniel Williamson
Changes:
m-file fixes, supplemental links, metadata updated

Version: 1.3 Jun 9, 2009 5:35 pm -0500 by Daniel Williamson
Changes:
updated links, images and accessibility

Version: 1.2 May 26, 2009 4:44 pm -0500 by Daniel Williamson
Changes:
fixed module names, and updated content structure

Version: 1.1 May 14, 2009 2:56 pm -0500 by Paul E Pfeiffer
Changes:
content

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Pfeiffer, P. (2009, September 18). Random Vectors and Joint Distributions. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/m23318/1.8/

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Pfeiffer, Paul. "Random Vectors and Joint Distributions." OpenStax_CNX. September 18, 2009. http://cnx.org/content/m23318/1.8/.

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Paul Pfeiffer, "Random Vectors and Joint Distributions," OpenStax_CNX, September 18, 2009, http://cnx.org/content/m23318/1.8/.

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Pfeiffer, P. 2009. Random Vectors and Joint Distributions. OpenStax_CNX, September 18, 2009. http://cnx.org/content/m23318/1.8/.

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